Question

For time t, the position of an object moving along the x-axis is given by

1/3 t² −2t ² +3t+1. Which of the following statements about the object is true at time t?

A) The object is at rest.

B) The object is moving in the positive direction.

C) The object is moving in the negative direction.

D) The object is experiencing constant acceleration.

Answer 1

The position of an object moving along the x-axis is given by the function x(t) = 1/3t^2 - 2t^2 + 3t + 1. To determine the motion of the object at time t, we need to analyze its velocity.

Step-by-step explanation:

The position of an object moving along the x-axis is given by the function x(t) = 1/3t^2 - 2t^2 + 3t + 1.

To determine the motion of the object at time t, we need to analyze its velocity. Velocity is the derivative of position with respect to time. Taking the derivative of x(t) gives us the velocity function v(t) = 2/3t - 4t + 3.

To determine the object's motion at time t, we need to evaluate the velocity function at that particular time. If v(t) > 0, the object is moving in the positive direction; if v(t) < 0, the object is moving in the negative direction. If v(t) = 0, the object is at rest. Therefore, the correct statement about the object at time t can be determined by evaluating the velocity function at that time.